Question: $J$ $K$ $L$ If: $ JK = 4x + 3$, $ JL = 47$, and $ KL = 9x + 5$, Find $KL$.
Solution: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {4x + 3} + {9x + 5} = {47}$ Combine like terms: $ 13x + 8 = {47}$ Subtract $8$ from both sides: $ 13x = 39$ Divide both sides by $13$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $KL$ $ KL = 9({3}) + 5$ Simplify: $ {KL = 27 + 5}$ Simplify to find ${KL}$ : $ {KL = 32}$